Aside from both using the Hardy–Stein identity, the proofs of Theorems REF  and REF  have distinct flavors. The former is mostly self-contained and avoids the abstract potential theory, in contrast to the approaches for \(p=2\)  in [1]} and [2]}. The setting of Theorem REF  is more delicate because we do not assume the existence of a boundary function \(g\) ; we need to construct it using traces of harmonic functions in Hardy and Sobolev spaces.
